<p><b>Abstract</b>—In this paper, we present a new scheduling approach for servicing soft aperiodic requests in a hard real-time environment, where a set of hard periodic tasks is scheduled using the Earliest Deadline First algorithm. The main characteristic of the proposed algorithm is that it achieves full processor utilization and optimal aperiodic responsiveness, still guaranteeing the execution of the periodic tasks. Another interesting feature of the proposed algorithm is that it can easily be tuned to balance performance versus complexity for adapting it to different application requirements. Schedulability issues, performance results, and implementation complexity of the algorithm are discussed and compared with other methods, such as Background, the Total Bandwidth Server, and the Slack Stealer. Resource reclaiming and extensions to more general cases are also considered. Extensive simulations show that a substantial improvement can be achieved with a little increase of complexity, ranging from the performance of the Total Bandwidth Server up to the optimal behavior.</p>